3 Answers
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"Late to" implies that you are present, but late enough that the "party" is already well underway. "Late for" implies that you haven't arrived yet (or have just arrived) and the "party" has started.

The respective connotations are that if you are "late to" a party, the best food and drink is gone, conversation groups and dance partners have formed which are harder to chisel into, people have already had a few drinks, and generally you have missed out on having the best time. This holds when used figuratively; a person who shows up to a sale after the item they wants is gone or the deadline has passed, or in business terms if a "late mover" enters a product market that is already in decline, they have "missed out" on getting the best deal or a good share of the revenue.

Being "late for the party" is less commonly used figuratively, but is often heard in context of a new person joining a group just before (or after) the group embarks on something: "Am I late for the party?". The connotation is that the "party" (the event in which the person wanted to participate) may or may not have begun; the speaker is asking which.

I believe the question here is being directed to the figurative use of the phrase. Being "late to the party" means most people became aware of something before you did, or adopted something before you did. For example:

Yesterday I set up a Facebook page. I guess I'm late to the party, hm?